Predicting on circular domains is a central issue in many industrial fields such as microelectronics and environmental engineering. In this context Gaussian process (GP) regression is used, coupled with Zernike polynomials. However, usual GP models do not take into account the geometry of the disk in their covariance structure (or kernel), which may be a drawback at least for technological or physical processes involving a rotation or a diffusion from the center of the disk. For that purpose, we introduce so-called polar GPs defined on the non-Euclidian space of polar coordinates. Their kernels are obtained as a combination of a kernel for the radius using an Euclidean distance, and a kernel for the angle, based on either chordal or geodesic distances on the unit circle. Their efficiency is illustrated on two industrial applications where radial and angular patterns are visible. In a second time, the problem of defining an initial design of experiment (DoE) for circular domains is considered. Two new Latin hypercube designs are obtained, by defining a valid maximin criterion for polar coordinates. Their robustness in prediction is assessed and compared to other DoEs over a range of various toy functions and models.